Figure 4. Many inhibitory neurons must be perturbed to evoke a paradoxical inhibitory response. A, Minimum proportion of the inhibitory population p/N that must be perturbed for the paradoxical effect to appear in the perturbed neurons in a network with equal numbers of excitatory and inhibitory neurons. This analytical result does not depend on the size of the network N. Parameters: {hI, hE, fI, τ} = {1, 1, 0.5, 10 ms}. B, Miminum proportion of inhibition p/NI for a network with fI = 20%. Other parameters: {hI, hE, τ, NE, NI} = {1, 1, 10 ms, 80, 20}. Note the difference in scale compared with A. C, Minimum proportion of the inhibitory population p/N that must be perturbed under for the paradoxical effect for networks with sparse synaptic connectivity between excitatory and inhibitory neurons. Note that this does not affect the overall trend for averaged response of stimulated inhibitory neurons (cf. B), but the stochastic effect of introducing sparse connections in smaller networks is evident. Parameters: {hEE, hEI, hIE, hII, NE, NI} = {0.1, 0.5, 0.5, 0.5, 4000, 1000}. “X” in B and C, estimated nominal parameters for mouse visual cortex {wE, wI} = {5.4, 56}. This estimate gives p/NI = 70%. †Non-ISN regime; ‡unstable regime.